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Sphericity and multiplication of double cosets for infinite-dimensional classical groups. (English. Russian original) Zbl 1271.22019
Funct. Anal. Appl. 45, No. 3, 225-239 (2011); translation from Funkts. Anal. Prilozh. 45, No. 3, 79-96 (2011).
Summary: We construct spherical subgroups in infinite-dimensional classical groups \(G\) (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets \(L\backslash G/L\) for various subgroups \(L\) in \(G\); these semigroups act in spaces of \(L\)-fixed vectors in unitary representations of \(G\). We also obtain semigroup envelops of groups \(G\) generalizing constructions of operator colligations.

MSC:
22E66 Analysis on and representations of infinite-dimensional Lie groups
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